In the ocean, most waves are created by the wind. The rushing air pushes some water molecules together, producing a swell of water -- a disturbance in the ocean's surface -- at a particular point. These molecules push on the molecules next to them, which push on the molecules next to them and so on. In this way, the disturbance is passed along the surface of the ocean, while the individual water molecules stay in roughly the same area.
There are a number of ways to replicate this type of wave action. All you need is a basin of water and some means of creating a periodic disturbance. You could use a strong blast of air along the surface, a rotating paddle wheel (like the ones used on steamboats) or an oscillating plunger. Basically, you push on the water at one point and this energy travels outward, through the surrounding water. This is the same thing that happens when you drop a rock into a pond.
Emerald Pointe features a wave pool of this sort at Splash Island, a swimming area for younger kids. In this pool, gentle ripples spread out from the deeper end, just under a volcano structure, and wash up on the small beach.
Let's take a look at the machinery that makes this happen.